Question
Prove the following by using the principle of mathematical induction for all 
Solution
Let P(n): 
I. For n = 1,
P(1) : 
∴ P(1) is true.
II. Suppose the statement is true for n = m, 
P(m): 
...(i)
III. For n = (m + 1),
P(m + 1) : 
or 
From (i),
∴ 
Which is true
∴ P(m + 1) is true
∴ P(m) is true 
P(m + 1) is true
Hence, by the principle of mathematical induction, statement P(n) is true for all 
